Name ______Class ______Date ______
TEKS 7BInvestigate and analyze characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate using the relationship
between wavespeed, frequency, and wavelength.
TEKS 7B: Wave Speed, Frequency, and Wavelength
What is a wave?
A wave is a disturbance that propagates through space and time, transporting energy. A mechanical wave is a disturbance or variation that travels through a medium. Electromagnetic waves, such as infrared radiation and visible light, do not need a medium. These waves can propagate through the vacuum of space. This is why you can see light from the sun and the stars and why you can feel the sun’s heat.
Waves transfer energy; they do not transfer matter. Think of “the wave” at a football game or the motion caused by the wind blowing across a field of tall grass. The individual elements—the fans in the stands or the blades of grass—do not actually travel; instead, it is the energy that moves from one place to another.
What are the two types of waves?
Transverse WavesIn transverse waves, the disturbance of the medium is perpendicular to the direction of wave travel. A good example of this is a wave on the string. The parts of the string move up and down, but the disturbance propagates perpendicularly to this motion.
Electromagnetic waves and water waves are two examples of transverse waves.
Longitudinal WavesIn longitudinal waves, the elements of the medium move back and forth in the same direction as the wave motion, and about an equilibrium point. Imagine a spring toy stretched between two children lying on the floor. If one child quickly pushes and pulls the spring in the direction in which the spring is stretched, you will see a propagation of compressed and expanded coils, known as compressions and rarefactions. The disturbance travels the length of the stretched spring.
Sound waves are longitudinal waves. In sound waves traveling in air, it is the distance between air molecules that decreases and increases as the wave propagates.
What are some wave characteristics?
Water waves, sound waves, electromagnetic waves, and waves on a string might not seem related, but they all have certain characteristics in common.
FrequencyThe frequency of a wave is the number of waves produced each secondby a source. It is also the number of waves that pass a certain point each second. The unit of measure for frequency is the hertz (Hz). Consider the figures below.
In the same time duration, the low-frequency wave, as shown on the left, has only a few vibrations, whereas the high-frequency wave, on the right, has many vibrations.
WavelengthThe wavelength of a wave is the distance between a point on one wave and the same point on the next wave. For example, a wavelength can be determined by findingeither (a) the distance between one crest of a wave and the next crest of a wave or (b) the distance from one trough of a wave to the next trough.
The amplitude of a wave is the vertical distance from the equilibrium line to either the crest or the trough, or half the vertical distance from trough to crest.
Wave SpeedWave speed is the speed at which the disturbance in the medium travels. Wave speed is a characteristic of the medium. For example, the speed of a wave on a string depends on the density and tension of the string itself. The speed of a sound in air depends on the temperature of the air.
What is the relationship between wavelength, frequency, and wave speed?
The relationship between wavelength, frequency, and wave speed is expressed in the following equation.
wave speed = frequency wavelength
This relationship holds true for all waves. The speed of electromagnetic waves in a vacuum is
3.0 108 m/s. The speed of sound in air at 20C is 343 m/s.
Example 1The frequency of the wave broadcasted by a radio station is 1.2 × 106 Hz. Calculate the wavelength of the station’s wave.
Given: frequency = 1.2 × 106 Hz
wave speed = 3.00 × 108 m/s
Unknown: wavelength
Equation: wave speed = wavelength × frequency
Solution: Solve the equation for wavelength:
Substitute the given values:
Example 2A radio station broadcasts a radio wave with a wavelength of 3.0 meters. Calculate the frequency of the wave.
Given: wavelength = 3.0 m
wave speed = 3.00×108 m/s
Unknown: frequency
Equation: wave speed = wavelength × frequency
Solution: Solve the equation for frequency:
Substitute the given values:
Example 3The frequency of a green laser beam is about 5.64 × 10-14Hz. While traveling through diamond, the frequency of the beam remains unchanged, but its wavelength is compressed from 532 nm to about 220 nm. Calculate the speed of light in diamond. Calculate the frequency of these waves.
Given: frequency = 5.64×10-14 Hz
wavelength = 220 nm
Unknown: wave speed
Equation: wave speed = wavelength × frequency
Solution: Substitute the given values:
wave speed = (5.64×10-14Hz)(220 nm)
= 124,000 km/s
Lesson Check
1.CalculateCalculate the speed of a wave with a wavelength of 650 nm and a frequency of
4.6 x 1016 Hz. (Recall that a nanometer—nm—is 10–9 m.)
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2.CalculateCalculate the wavelength of a wave with a frequency of 145 Hz and a wave speed of
450 m/s.
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3.CalculateCalculate the frequency of a wave with a wavelength of 1.75 cm and a speed of
12.6 cm/s.
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4.One way to measure the speed of light is to use your microwave oven and a bag of marshmallows. The procedure is as follows:
- Cover the bottom of a microwavable casserole dish with marshmallows.
- Remove the rotating plate from inside the microwave oven.
- Put the dish in the microwave and cook on low heat.
- Heat the marshmallows until they begin to melt in four or five spots, and then use oven mitts to remove the dish from the oven.
- Carefully measure the distance from one melted spot to another. This distance corresponds to half of the wavelength of the waves generated by the oven.
CalculateUsing this information, calculate the speed of light.
Suppose you measured the distance between melted spots and found it to be 6.3 cm. Note that most microwave ovens operate at 2,450 MHz (or 2.450 x 109 Hz).
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